Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols

Authors:
Leiba Rodman, Ilya M. Spitkovsky and Hugo J. Woerdeman

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1365-1370

MSC (2000):
Primary 47B35, 43A60

Published electronically:
September 19, 2001

MathSciNet review:
1879958

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.

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Algebras of convolution type operators with discrete groups of shifts and oscillating coefficients.

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Additional Information

**Leiba Rodman**

Affiliation:
Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795

Email:
lxrodm@math.wm.edu

**Ilya M. Spitkovsky**

Affiliation:
Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795

Email:
ilya@math.wm.edu

**Hugo J. Woerdeman**

Affiliation:
Department of Mathematics, The College of William and Mary, P.O. Box 8795, Williamsburg, Virginia 23187-8795

Email:
hugo@math.wm.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06276-1

Keywords:
Almost periodic functions,
Toeplitz operators,
Fredholmness

Received by editor(s):
October 28, 2000

Published electronically:
September 19, 2001

Additional Notes:
The research of all three authors was partially supported by NSF grant DMS-9988579.

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2001
American Mathematical Society